The continuously infinite group ∞1 is omitted.
| Coordinates | Seitz symbol |
|---|---|
| a, b, c | x, y, z | { 1 ‖ 1 | 0 } |
| a+1/2, -b, -c+1/2 | x, y, z | { 1 ‖ 2100 | 1/2 0 1/2 } |
| -a, b, -c+1/2 | x, y, z | { 1 ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b, c | x, y, z | { 1 ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | -x, -y, -z | { -1 ‖ -1 | 0 } |
| -a+1/2, b, c+1/2 | -x, -y, -z | { -1 ‖ m100 | 1/2 0 1/2 } |
| a, -b, c+1/2 | -x, -y, -z | { -1 ‖ m010 | 0 0 1/2 } |
| a+1/2, b, -c | -x, -y, -z | { -1 ‖ m001 | 1/2 0 0 } |
| a, b, c | -x, y, z | { m ‖ 1 | 0 } |
| a+1/2, -b, -c+1/2 | -x, y, z | { m ‖ 2100 | 1/2 0 1/2 } |
| -a, b, -c+1/2 | -x, y, z | { m ‖ 2010 | 0 0 1/2 } |
| -a+1/2, -b, c | -x, y, z | { m ‖ 2001 | 1/2 0 0 } |
| -a, -b, -c | x, -y, -z | { 2 ‖ -1 | 0 } |
| -a+1/2, b, c+1/2 | x, -y, -z | { 2 ‖ m100 | 1/2 0 1/2 } |
| a, -b, c+1/2 | x, -y, -z | { 2 ‖ m010 | 0 0 1/2 } |
| a+1/2, b, -c | x, -y, -z | { 2 ‖ m001 | 1/2 0 0 } |
| WP | Site symmetry | Representative |
|---|---|---|
| 4a | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,0,0 | 0,0,0) |
| 4b | $\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $ | (0,1/2,0 | 0,0,0) |
| 4c | $.\ce{^{1}{2}}.\ce{^{\infty m}{1}} $ | (0,b,1/4 | 0,0,z) |
| 4d | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,0,c | 0,0,z) |
| 4e | $..\ce{^{1}{2}}\ce{^{\infty m}{1}} $ | (1/4,1/2,c | 0,0,z) |
| 8f | $\ce{^{1}{1}}\ce{^{\infty m}{1}} $ | (a,b,c | 0,0,z) |
| Wavevector-k | Little co-group |
|---|---|
| Γ:(0,0,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| R:(1/2,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| S:(1/2,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| T:(0,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| U:(1/2,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| X:(1/2,0,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Y:(0,1/2,0) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| Z:(0,0,1/2) | $ \ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{-1}{m}}\ce{^{\infty m}{1}} $ |
| A:(u,0,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| B:(0,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| C:(u,1/2,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| D:(1/2,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Δ:(0,v,0) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| E:(u,1/2,1/2) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| G:(1/2,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| H:(0,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Λ:(0,0,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| P:(1/2,v,1/2) | $ \ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| Q:(1/2,1/2,w) | $ \ce{^{2}{m}}\ce{^{2}{m}}\ce{^{-1}{m}}\ce{^{\infty}{1}} $ |
| Σ:(u,0,0) | $ \ce{^{-1}{m}}\ce{^{2}{m}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| K:(0,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| L:(1/2,v,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| M:(u,0,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| N:(u,1/2,w) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| V:(u,v,0) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| W:(u,v,1/2) | $ \ce{^{m}{2/}}\ce{^{2}{m}}\ce{^{\infty}{1}} $ |
| GP:(u,v,w) | $ \ce{^{-1}{-1}}\ce{^{\infty}{1}} $ |
Spin Brillouin Zone
| k-vector | k-vector-G↑ | A↑G(4) |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{3}^{S}(2) $ |
| R:(1/2,1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4) $ |
| S:(1/2,1/2,0) | T:(0,1/2,1/2) | $(S)T_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(2)⊕(T)S_{3}^{S}(2) $ |
| U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{1}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(2)⊕Y_{3}^{S}(2) $ |
| Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{1}^{S}(2)⊕(Z)X_{3}^{S}(2) $ |
| A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ |
| B:(0,v,-1/2) | D:(1/2,v,0) | $(B)D_{1}^{S}(2)⊕(B)D_{2}^{S}(2) $ |
| C:(u,1/2,0) | H:(0,1/2,u) | $(C)H_{1}^{S}(2)⊕(C)H_{2}^{S}(2) $ |
| D:(1/2,v,0) | B:(0,v,1/2) | $(D)B_{1}^{S}B_{2}^{S}(4) $ |
| Δ:(0,v,0) | Δ:(0,v,0) | $Δ_{1}^{S}(2)⊕Δ_{2}^{S}(2) $ |
| E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(2)⊕(E)Q_{2}^{S}(2) $ |
| G:(1/2,0,w) | A:(-w,0,1/2) | $(G)A_{1}^{S}A_{2}^{S}(4) $ |
| H:(0,1/2,w) | C:(-w,1/2,0) | $2(H)C_{1}^{S}(2) $ |
| Λ:(0,0,w) | Σ:(-w,0,0) | $2(Λ)Σ_{1}^{S}(2) $ |
| P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
| Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $(Q)E_{1}^{S}E_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ |
| K:(0,v,w) | V:(-w,v,0) | $2(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-w,v,1/2) | $(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | M:(-w,0,u) | $2M_{1}^{S}(2) $ |
| N:(u,1/2,w) | N:(-w,1/2,u) | $2N_{1}^{S}(2) $ |
| V:(u,v,0) | K:(0,v,u) | $2(V)K_{1}^{S}(2) $ |
| W:(u,v,-1/2) | L:(1/2,v,u) | $2(W)L_{1}^{S}(2) $ |
| GP:(u,v,w) | GP:(-w,v,u) | $2GP_{1}^{S}(2) $ |
| k-vector | k-vector-G↑ | A↑G(4) |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2) $ |
| R:(1/2,1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4) $ |
| S:(1/2,1/2,0) | T:(0,1/2,1/2) | $(S)T_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(2)⊕(T)S_{4}^{S}(2) $ |
| U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{1}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(2)⊕Y_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{1}^{S}(2)⊕(Z)X_{4}^{S}(2) $ |
| A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ |
| B:(0,v,-1/2) | D:(1/2,v,0) | $2 (B)D_{1}^{S}(2) $ |
| C:(u,1/2,0) | H:(0,1/2,u) | $(C)H_{1}^{S}(2)⊕(C)H_{2}^{S}(2) $ |
| D:(1/2,v,0) | B:(0,v,1/2) | $(D)B_{1}^{S}B_{2}^{S}(4) $ |
| Δ:(0,v,0) | Δ:(0,v,0) | $2 Δ_{1}^{S}(2) $ |
| E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(2)⊕(E)Q_{2}^{S}(2) $ |
| G:(1/2,0,w) | A:(-w,0,1/2) | $(G)A_{1}^{S}A_{2}^{S}(4) $ |
| H:(0,1/2,w) | C:(-w,1/2,0) | $(H)C_{1}^{S}(2)⊕(H)C_{2}^{S}(2) $ |
| Λ:(0,0,w) | Σ:(-w,0,0) | $(Λ)Σ_{1}^{S}(2)⊕(Λ)Σ_{2}^{S}(2) $ |
| P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
| Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $(Q)E_{1}^{S}E_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ |
| K:(0,v,w) | V:(-w,v,0) | $2(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-w,v,1/2) | $(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | M:(-w,0,u) | $2M_{1}^{S}(2) $ |
| N:(u,1/2,w) | N:(-w,1/2,u) | $2N_{1}^{S}(2) $ |
| V:(u,v,0) | K:(0,v,u) | $2(V)K_{1}^{S}(2) $ |
| W:(u,v,-1/2) | L:(1/2,v,u) | $2(W)L_{1}^{S}(2) $ |
| GP:(u,v,w) | GP:(-w,v,u) | $2GP_{1}^{S}(2) $ |
| k-vector | k-vector-G↑ | A↑G(4) |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{4}^{S}(2) $ |
| R:(1/2,1/2,-1/2) | R:(1/2,1/2,1/2) | $R_{1}^{S}(4) $ |
| S:(1/2,1/2,0) | T:(0,1/2,1/2) | $(S)T_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{2}^{S}(2)⊕(T)S_{3}^{S}(2) $ |
| U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $U_{1}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $(X)Z_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(2)⊕Y_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{2}^{S}(2)⊕(Z)X_{3}^{S}(2) $ |
| A:(u,0,-1/2) | G:(1/2,0,u) | $(A)G_{1}^{S}(2)⊕(A)G_{2}^{S}(2) $ |
| B:(0,v,-1/2) | D:(1/2,v,0) | $2(B)D_{2}^{S}(2) $ |
| C:(u,1/2,0) | H:(0,1/2,u) | $(C)H_{1}^{S}(2)⊕(C)H_{2}^{S}(2) $ |
| D:(1/2,v,0) | B:(0,v,1/2) | $(D)B_{1}^{S}B_{2}^{S}(4) $ |
| Δ:(0,v,0) | Δ:(0,v,0) | $2 Δ_{1}^{S}(2) $ |
| E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $(E)Q_{1}^{S}(2)⊕(E)Q_{2}^{S}(2) $ |
| G:(1/2,0,w) | A:(-w,0,1/2) | $(G)A_{1}^{S}A_{2}^{S}(4) $ |
| H:(0,1/2,w) | C:(-w,1/2,0) | $(H)C_{1}^{S}(2)⊕(H)C_{2}^{S}(2) $ |
| Λ:(0,0,w) | Σ:(-w,0,0) | $(Λ)Σ_{1}^{S}(2)⊕(Λ)Σ_{2}^{S}(2) $ |
| P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $P_{1}^{S}P_{2}^{S}(4) $ |
| Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $(Q)E_{1}^{S}E_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $(Σ)Λ_{1}^{S}(2)⊕(Σ)Λ_{2}^{S}(2) $ |
| K:(0,v,w) | V:(-w,v,0) | $2(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-w,v,1/2) | $(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | M:(-w,0,u) | $2M_{1}^{S}(2) $ |
| N:(u,1/2,w) | N:(-w,1/2,u) | $2N_{1}^{S}(2) $ |
| V:(u,v,0) | K:(0,v,u) | $2(V)K_{1}^{S}(2) $ |
| W:(u,v,-1/2) | L:(1/2,v,u) | $2(W)L_{1}^{S}(2) $ |
| GP:(u,v,w) | GP:(-w,v,u) | $2GP_{1}^{S}(2) $ |
| k-vector | k-vector-G↑ | A↑G(8) |
| Γ:(0,0,0) | Γ:(0,0,0) | $Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2)⊕Γ_{3}^{S}(2)⊕Γ_{4}^{S}(2) $ |
| R:(1/2,1/2,-1/2) | R:(1/2,1/2,1/2) | $2R_{1}^{S}(4) $ |
| S:(1/2,1/2,0) | T:(0,1/2,1/2) | $2(S)T_{1}^{S}(4) $ |
| T:(0,1/2,-1/2) | S:(1/2,1/2,0) | $(T)S_{1}^{S}(2)⊕(T)S_{2}^{S}(2)⊕(T)S_{3}^{S}(2)⊕(T)S_{4}^{S}(2) $ |
| U:(1/2,0,-1/2) | U:(1/2,0,1/2) | $2U_{1}^{S}(4) $ |
| X:(1/2,0,0) | Z:(0,0,1/2) | $2(X)Z_{1}^{S}(4) $ |
| Y:(0,1/2,0) | Y:(0,1/2,0) | $Y_{1}^{S}(2)⊕Y_{2}^{S}(2)⊕Y_{3}^{S}(2)⊕Y_{4}^{S}(2) $ |
| Z:(0,0,-1/2) | X:(1/2,0,0) | $(Z)X_{1}^{S}(2)⊕(Z)X_{2}^{S}(2)⊕(Z)X_{3}^{S}(2)⊕(Z)X_{4}^{S}(2) $ |
| A:(u,0,-1/2) | G:(1/2,0,u) | $2(A)G_{1}^{S}(2)⊕2(A)G_{2}^{S}(2) $ |
| B:(0,v,-1/2) | D:(1/2,v,0) | $2(B)D_{1}^{S}(2)⊕2(B)D_{2}^{S}(2) $ |
| C:(u,1/2,0) | H:(0,1/2,u) | $2(C)H_{1}^{S}(2)⊕2(C)H_{2}^{S}(2) $ |
| D:(1/2,v,0) | B:(0,v,1/2) | $2(D)B_{1}^{S}B_{2}^{S}(4) $ |
| Δ:(0,v,0) | Δ:(0,v,0) | $2Δ_{1}^{S}(2)⊕2Δ_{2}^{S}(2) $ |
| E:(u,1/2,-1/2) | Q:(1/2,1/2,u) | $2(E)Q_{1}^{S}(2)⊕2(E)Q_{2}^{S}(2) $ |
| G:(1/2,0,w) | A:(-w,0,1/2) | $2(G)A_{1}^{S}A_{2}^{S}(4) $ |
| H:(0,1/2,w) | C:(-w,1/2,0) | $2(H)C_{1}^{S}(2)⊕2(H)C_{2}^{S}(2) $ |
| Λ:(0,0,w) | Σ:(-w,0,0) | $2(Λ)Σ_{1}^{S}(2)⊕2(Λ)Σ_{2}^{S}(2) $ |
| P:(1/2,v,-1/2) | P:(1/2,v,1/2) | $2P_{1}^{S}P_{2}^{S}(4) $ |
| Q:(1/2,1/2,w) | E:(-w,1/2,1/2) | $2(Q)E_{1}^{S}E_{2}^{S}(4) $ |
| Σ:(u,0,0) | Λ:(0,0,u) | $2(Σ)Λ_{1}^{S}(2)⊕2(Σ)Λ_{2}^{S}(2) $ |
| K:(0,v,w) | V:(-w,v,0) | $4(K)V_{1}^{S}(2) $ |
| L:(1/2,v,w) | W:(-w,v,1/2) | $2(L)W_{1}^{S}W_{1}^{S}(4) $ |
| M:(u,0,w) | M:(-w,0,u) | $4M_{1}^{S}(2) $ |
| N:(u,1/2,w) | N:(-w,1/2,u) | $4N_{1}^{S}(2) $ |
| V:(u,v,0) | K:(0,v,u) | $4(V)K_{1}^{S}(2) $ |
| W:(u,v,-1/2) | L:(1/2,v,u) | $4(W)L_{1}^{S}(2) $ |
| GP:(u,v,w) | GP:(-w,v,u) | $4GP_{1}^{S}(2) $ |